Maximizing Mutual Information, as is required by (REF ), is a notoriously difficult problem that arises in many domains, and there is a large collection of approximations and bounds in the literature [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Here, we seek an approximation to Mutual Information that does not require knowing \({\rm m}(\mathbf {x})\) , that requires only local information about \(\psi (\theta )\) , and that can be evaluated separately for each \(\theta \) . These properties will allow us to use MCMC methods to serially sample \(\theta \)  values from \(\psi (\theta )\) .
